Berkson and Porta [1]} give the following criterion for
an analytic function \(G\)  to generate a one-parameter semigroup
of analytic mappings of the right half-plane \({\mathbb {C}}_+\)  to itself; that is, solutions to
\(\frac{\partial \varphi _t(z)}{\partial t}=G(\varphi _t(z)), \qquad \varphi _0(z)=z,\) 
